A frequency table shows the number of pets owned by pupils. Number of pets: 0, 1, 2 Frequency: 4, 3, 3 Write down the mode.
(1)
6
A grouped frequency table has class intervals 0-4, 5-9, 10-14 with frequencies 6, 9, 2. Write down the modal class.
(1)
7
A survey of 10 pupils records the number of siblings each has. Number of siblings: 0, 1, 2, 3 Frequency: 3, 4, 2, 1 Calculate the mean number of siblings.
(2)
8
A frequency table shows: Value: 5, 6, 7, 8 Frequency: 2, 4, 3, 3 Find the median value.
(2)
9
Estimate the mean from this grouped frequency table. Class intervals: 0-9, 10-19 Frequency: 5, 5
(2)
10
A set of 6 numbers has a mean of 9. Find the total sum of the 6 numbers.
(2)
11
The mean of 4 numbers is 7. Three of the numbers are 5, 9 and 6. Find the fourth number.
(2)
12
A frequency table shows: Value: 20, 21, 22, 23 Frequency: 3, 5, 4, 4 Find the median value.
(2)
13
A frequency table shows: Value: 2, 3, 4 Frequency: 5, 3, 2 Calculate the mean.
(2)
14
A grouped frequency table has class intervals 0-9, 10-19, 20-29 with frequencies 4, 10, 6. State the modal class and explain why the exact mode cannot be found from this table.
(2)
15
A class of 20 pupils has a mean test score of 55. One pupil, who scored 30, leaves and is replaced by a new pupil who scores 60. Work out the new mean test score for the class.
(3)
16
A survey of 15 households records the number of cars owned. Number of cars: 0, 1, 2, 3 Frequency: 3, 6, 4, 2 Find the median number of cars per household.
(3)
17
A gym records the time, in minutes, that 20 members spent on a treadmill. Class intervals: 0-19, 20-39, 40-59 Frequency: 6, 9, 5 Estimate the mean time spent on the treadmill.
(3)
18
A frequency table for the number of texts sent by 25 pupils shows: Number of texts: 2, 3, 4 Frequency: 8, m, 6 Find m, then work out the mean number of texts sent.
(3)
19
Two factory shifts recorded their average packing times. Shift A: median = 18 minutes, mean = 19.5 minutes. Shift B: median = 20 minutes, mean = 20.2 minutes. State which shift's packing times are more likely to be skewed and justify your answer.
(3)
20
The mean of 18 numbers is 12. Three of these numbers, with a mean of 8, are removed. Find the mean of the remaining 15 numbers.
(3)
Mark scheme · KS3.M-S5D Averages from Frequency Tables: Fluency and Exam Drill
Question 1
B1 mean = 7 cao
Answer: 7
Question 2
B1 mode = 4 cao
Answer: 4
Question 3
B1 median = 4 cao
Answer: 4
Question 4
B1 median = 7 cao
Answer: 7
Question 5
B1 mode = 0 cao
Answer: 0
Question 6
B1 modal class 5-9 cao
Answer: 5-9
Question 7
M1 sum of value x frequency = 11 or equivalent method shown
A1 mean = 1.1 cao
Answer: 1.1
Question 8
M1 correct cumulative frequencies and locating the middle position(s)
A1 median = 6.5 cao
Answer: 6.5
Question 9
M1 uses midpoints 4.5 and 14.5 multiplied by frequency
A1 mean = 9.5 cao
Answer: 9.5
Question 10
M1 recognises sum = mean x number of values
A1 54 cao
Answer: 54
Question 11
M1 total for 4 numbers = 28 and sum of the three known numbers = 20
A1 fourth number = 8 cao
Answer: 8
Question 12
M1 correct cumulative frequencies and locating the middle position(s)
A1 median = 21.5 cao
Answer: 21.5
Question 13
M1 sum of value x frequency = 27 or equivalent method shown
A1 mean = 2.7 cao
Answer: 2.7
Question 14
B1 modal class 10-19 cao
B1 reason: data are grouped so individual values inside the class are unknown, so the exact mode cannot be found
Answer: modal class 10-19; exact mode unknown because grouped data hide the individual values
Question 15
M1 original total = 20 x 55 = 1100
M1 new total = 1100 - 30 + 60 = 1130
A1 new mean = 56.5 cao
Answer: 56.5
Question 16
M1 correct cumulative frequencies shown
M1 identifies the median position as the 8th value out of 15
A1 median = 1 cao
Answer: 1
Question 17
M1 midpoints 9.5, 29.5 and 49.5 identified
M1 sum of fx = 570 calculated
A1 mean = 28.5 cao
Answer: 28.5
Question 18
M1 m = 25 - 8 - 6 = 11
M1 sum of value x frequency = 73
A1 mean = 2.92 cao
Answer: m = 11; mean = 2.92
Question 19
M1 calculates or compares the gap between mean and median for each shift
M1 states that a bigger gap between mean and median suggests more skew
A1 concludes Shift A is more likely skewed because its mean-median gap (1.5) is larger than Shift B's (0.2)
Answer: Shift A is more likely to be skewed
Question 20
M1 total of the 18 numbers = 216
M1 remaining sum = 216 - 24 = 192 and remaining count = 15