Statistics

A school trip organiser records how many students choose each activity using a chart where one whole boot symbol represents 4 students and a half boot represents 2 students. What type of chart is this?

• Aa pictogram✓
• Ba frequency table
• Ca bar chart
• Da pie chart

Answer: A pictogram uses repeated symbols, where part of a symbol can represent a smaller amount, to show quantities. A frequency table lists counts in rows rather than showing any symbols, so it does not fit this description. A pie chart divides a circle into slices and a bar chart uses the height of solid bars, so neither uses picture symbols either.

A vertical line chart shows the number of goals scored by a hockey team in each of their last 10 matches. How does this type of chart display each value?

• Aas a wide solid bar
• Bas a single thin line rising from the axis to the value✓
• Cas a slice cut from a circle
• Das a repeated picture symbol

Answer: In a vertical line chart, each data value is marked by a thin vertical line reaching up to the correct height, which makes it easy to compare individual values. Slices belong to pie charts, and repeated symbols belong to pictograms, not line charts. A wide solid bar is the feature of a bar chart, which uses thickness rather than a thin line.

Twenty pupils were asked how many pets they own. The frequency table shows: 0 pets, 6 pupils; 1 pet, 8 pupils; 2 pets, 4 pupils; 3 pets, 2 pupils. What is the modal number of pets?

• A3 pets
• B2 pets
• Cnone
• D1 pet✓

Answer: The mode is the value with the highest frequency, and 1 pet was owned by 8 pupils, which is more than any other number of pets. Owning 0 pets only had a frequency of 6, so it is not the mode. Owning 2 pets or 3 pets had even lower frequencies of 4 and 2, so neither can be the mode.

In a maths quiz, five friends scored 14, 18, 12, 20 and 16 out of 20. What is the mean score?

• A18
• B17
• C15
• D16✓

Answer: The mean is found by adding all five scores to get 80 and dividing by the number of friends, 5, which gives 16. Getting 15 would happen if the total were divided by the wrong number of friends. Getting 17 or 18 could result from adding the scores incorrectly before dividing.

A netball team's weekly training times in minutes are 45, 50, 40, 55 and 60. What is the median training time?

• A50 minutes✓
• B52.5 minutes
• C55 minutes
• D47.5 minutes

Answer: To find the median, the five times are placed in order as 40, 45, 50, 55 and 60, and the middle value is 50 minutes. Choosing 47.5 minutes or 52.5 minutes comes from averaging the wrong pair of numbers in the ordered list instead of simply identifying the middle one. Choosing 55 minutes picks a value above the true middle rather than the middle itself.

Six cyclists recorded these distances in kilometres for a Sunday ride: 12, 15, 18, 20, 22, 25. What is the median distance?

• A21 km
• B23.5 km
• C19 km✓
• D18.5 km

Answer: With six values there is no single middle number, so the median is the mean of the two middle values once the data is in order (18 and 20), giving 19 km. Averaging the two largest values (22 and 25) instead of the middle pair gives 23.5 km, averaging the 4th and 5th values (20 and 22) instead of the 3rd and 4th gives 21 km, and averaging the 2nd and 5th values (15 and 22) gives 18.5 km.

A gardener measures the heights of seven sunflowers in centimetres: 120, 135, 128, 200, 130, 125, 132. What is the range of these heights?

• A85 cm
• B265 cm
• C80 cm✓
• D320 cm

Answer: The range is the difference between the largest and smallest values, and 200 minus 120 gives 80 cm. Getting 320 cm or 265 cm comes from adding two of the heights together instead of subtracting the smallest from the largest. Getting 85 cm suggests the largest or smallest value was misread from the list.

In the sunflower data above, the tallest plant measured 200 cm, much taller than the rest, which were all under 140 cm. What is this unusually tall measurement called, and how does it affect the mean height?

• Athe range, and it pulls the mean higher than most of the data
• Bthe mode, and it pulls the mean lower than most of the data
• Can outlier, and it pulls the mean higher than most of the data✓
• Dthe median, and it has no effect on the mean at all

Answer: A value that is much higher or lower than the rest of the data is called an outlier, and because the mean uses every value in its calculation, one very large number pulls the mean upward. The median is the middle value once the data is ordered, not an unusual value, and only extreme changes near the middle affect it much. The mode is the most frequently occurring value and the range is the spread between the highest and lowest values, so neither name correctly describes 200 cm here.

In a survey of 60 pupils, 15 chose football as their favourite sport. If this is shown as a sector of a pie chart, how many degrees should the sector for football cover?

• A60 degrees
• B45 degrees
• C120 degrees
• D90 degrees✓

Answer: The sector angle is found by multiplying the fraction of pupils, 15 out of 60, by the 360 degrees in a full circle, giving 90 degrees. Getting 60 degrees would come from treating the fraction as a sixth rather than a quarter of the pupils. Getting 120 degrees or 45 degrees would come from multiplying by the wrong fraction, such as a third or an eighth, of the total.

A bar chart shows the number of books read last month by four friends: Amir 6, Beth 9, Carys 4, Dev 7. How many more books did Beth read than Carys?

• A15
• B3
• C5✓
• D13

Answer: The difference is found by subtracting the smaller bar from the larger one, so 9 minus 4 gives 5 more books. Getting 15 or 13 comes from adding two of the totals together instead of subtracting them. Getting 3 confuses Carys's total with Dev's total in the subtraction.

A frequency table for the shoe sizes of a class totals 30 pupils. The frequencies given are: size 4, 5 pupils; size 5, 9 pupils; size 6, 8 pupils; size 7, unknown. What is the missing frequency for size 7?

• A22
• B25
• C8✓
• D7

Answer: The four frequencies must add up to the total of 30 pupils, and 5 plus 9 plus 8 equals 22, so the missing frequency is 30 minus 22, which is 8. Getting 22 confuses the sum of the three known frequencies with the missing one itself. Getting 25 comes from subtracting only one of the other frequencies from 30 instead of all three, and getting 7 comes from a small slip in the final subtraction.

A grouped frequency table for the ages of visitors to a museum shows: 0-9 years, 25 visitors; 10-19 years, 12 visitors; 20-29 years, 18 visitors; 30-39 years, 9 visitors. What is the modal class?

• A0-9 years✓
• B20-29 years
• C10-19 years
• D30-39 years

Answer: The modal class is the group with the highest frequency, and 0 to 9 years has 25 visitors, more than any other group. The 10 to 19 years group only has 12 visitors, well below the highest count. The 20 to 29 years and 30 to 39 years groups have 18 and 9 visitors, both lower than the 0 to 9 years group.

A scatter graph plots the number of hours pupils spent revising against their test scores. The points rise from bottom-left to top-right in a fairly straight pattern. What does this suggest about the relationship between revision time and test score?

• Arevision time has no connection with test score at all
• Bmore revision time is generally linked with a higher test score✓
• Ctest score determines revision time
• Dmore revision time is generally linked with a lower test score

Answer: Points rising from bottom-left to top-right show a positive correlation, meaning that as one variable increases, the other tends to increase too, so more revision is generally linked with higher scores. A downward pattern from top-left to bottom-right would instead show revision linked with lower scores, which is not what is described. Scattered points with no clear pattern would show no connection, and a scatter graph on its own cannot prove which variable causes the other.

A scatter graph compares the outdoor temperature each day with the number of hot chocolates sold at a cafe. The points fall from top-left to bottom-right. What does this pattern show?

• Aas temperature rises, more hot chocolates tend to be sold
• Bas temperature rises, fewer hot chocolates tend to be sold✓
• Ctemperature and hot chocolate sales rise together at the same rate
• Dthere is no link between temperature and hot chocolate sales

Answer: Points falling from top-left to bottom-right show a negative correlation, so as one value increases the other tends to decrease, meaning fewer hot chocolates are sold as it gets warmer. An upward pattern would instead mean sales increase with temperature, which is the opposite of what is described. Points with no clear pattern would show no connection between the two variables, which does not match a clear falling trend.

Two classes sat the same spelling test out of 20. Class A's scores have a mean of 14 and a range of 4. Class B's scores have a mean of 14 and a range of 12. Which class had more consistent scores?

• Aneither class, because both classes have exactly the same mean
• BClass B, because its larger range shows less spread in the scores
• CClass A, because its mean is higher than Class B's mean
• DClass A, because its smaller range shows less spread in the scores✓

Answer: Consistency is measured by how spread out the scores are, and a smaller range means the scores are closer together, so Class A with a range of 4 was more consistent than Class B with a range of 12. A larger range shows more spread, not less, so that reasoning about Class B is incorrect. Both classes share the same mean of 14, so the mean cannot be used to tell them apart, and equal means do not mean the spread of scores is also equal.