Write down the mean, median and mode for each small frequency table.
(a)Data values: 2, 3, 3, 5(1)
(b)Data values: 4, 4, 6(1)
(c)Data values: 1, 2, 5, 6, 6(1)
(d)Data values: 7, 7, 8, 9(1)
2
A teacher records the number of books read by four pupils: Alice 3, Ben 5, Priya 2, Kwame 4. Calculate the mean number of books read.
(2)
3
Use the frequency table to write down the mode, then find the median. Value: 10, 11, 12, 13 Frequency: 2, 3, 1, 4
(a)Write down the mode.(1)
(b)Find the median value.(2)
4
A small football club records goals scored in 5 matches: goals 0,1,2,3 with frequencies 1,2,1,1 respectively. Calculate the mean number of goals per match.
(2)
5
From the frequency table below, find the median. Score: 2, 3, 4, 5, 6 Frequency: 1, 2, 4, 2, 1
(2)
6
Write down the modal class from this grouped frequency table. Class intervals: 0-9, 10-19, 20-29 Frequency: 3, 7, 4
(1)
7
The table shows how many pets pupils in a class have. Number of pets: 0, 1, 2, 3 Frequency: 5, 8, 4, 3 Find the mean number of pets per pupil.
(3)
8
A frequency table lists shoe sizes of 12 pupils. Sizes 3,4,5,6 have frequencies 2,3,4,3. Find the median shoe size.
(2)
9
From the table: Marks 0, 1, 2, 3 with frequencies 1, 4, 4, 1. (a) State the mode. (b) Find the mean.
(a)State the mode.(1)
(b)Find the mean.(1)
10
A class of 15 pupils has scores with mean 12. One pupil with score 20 leaves and is replaced by a new pupil with score 8. Explain how the class mean changes and calculate the new mean.
(3)
11
Estimate the mean from this grouped frequency table where class widths are 10. Class: 0-9, 10-19, 20-29, 30-39 Frequency: 4, 6, 3, 2
(3)
12
Using the grouped frequency table with classes 0-9, 10-19, 20-29 and frequencies 2, 5, 3, find the modal class and explain why we cannot give an exact mode.
(2)
13
A frequency table shows marks 5, 6, 7 with frequencies 3, f, 4. The mean mark is 6.1. Find f.
(3)
14
Two classes sat the same test. Class A median = 14, mean = 13.5. Class B median = 12, mean = 13. Decide which class is more likely to have a skewed distribution and explain your reasoning briefly.
(3)
15
A cumulative frequency table of test times (minutes) shows: Time ≤ 10: 2 Time ≤ 20: 6 Time ≤ 30: 11 Time ≤ 40: 15 Find the lower quartile (25th percentile) time.
(2)
16
A school orders 60 identical exercise books. A survey of 30 pupils gave a frequency table for pages used last term: pages used 10, 20, 30, 40 with frequencies 6, 12, 9, 3. Using this table, estimate how many pages a randomly chosen pupil from the 60-pupil year might use on average.
(3)
17
Stretch: A grouped table gives class intervals 1-3, 4-6, 7-9 with frequencies 5, 12, 8. Use the modal class to estimate the mode using linear interpolation within the modal class. The modal class is 4-6. Show your working and give your answer to 1 decimal place.
(4)
18
Stretch: Which average, mean or median, would you quote for typical weekly pocket money if the distribution is strongly skewed by a few pupils with very large amounts? Give a short justification.
(3)
Mark scheme · KS3.M-S5 Averages from Frequency Tables
Question 1
(a) B1 mean = 3.25, median = 3, mode = 3 cao
(a) Answer: mean 3.25; median 3; mode 3
(b) B1 mean = 14/3, median = 4, mode = 4 cao
(b) Answer: mean 14/3; median 4; mode 4
(c) B1 mean = 20/5, median = 5, mode = 6 cao
(c) Answer: mean 4; median 5; mode 6
(d) B1 mean = 7.75, median = 7.5, mode = 7 cao
(d) Answer: mean 7.75; median 7.5; mode 7
Question 2
M1 sum of values 3 + 5 + 2 + 4 = 14 or method to divide by 4 shown
A1 mean = 3.5 cao
Answer: 3.5
Question 3
(a) B1 mode = 13 cao
(a) Answer: 13
(b) M1 correct cumulative frequencies and locating middle position (total frequency 10 so median is 5th and 6th values)
(b) A1 median = 11.5 cao
(b) Answer: 11.5
Question 4
M1 use of sum value*frequency: 0*1 + 1*2 + 2*1 + 3*1 = 0 + 2 + 2 + 3 = 7
A1 mean = 7/5 = 1.4 cao
Answer: 1.4
Question 5
M1 correct cumulative frequency and middle position: total = 10 so median is average of 5th and 6th values
M1 state which class likely skewed (Class B because mean > median or vice versa) or show relationship
M1 explain idea: mean is affected by extreme values so differs from median when skewed
A1 conclude Class B is likely positively skewed because mean (13) is greater than median (12) or Class A near symmetric since mean 13.5 close to median 14
Answer: Class B more likely skewed; mean > median suggests positive skew
Question 15
M1 identify total frequency 15 and 25% position = 0.25*15 = 3.75 so look for 4th value in cumulative table
A1 lower quartile = 20 minutes cao
Answer: 20
Question 16
M1 compute mean from sample: sum = 10*6 + 20*12 + 30*9 + 40*3 = 60 + 240 + 270 + 120 = 690
M1 divide by sample size 30 to get mean = 690/30 = 23
A1 estimate for 60 pupils = 23 pages on average per pupil cao
Answer: 23
Question 17
M1 identify modal class 4-6 and write class width = 3, f1 = frequency of modal class = 12, f0 = previous class freq = 5, f2 = next class freq = 8
M1 write interpolation formula estimate mode = L + ((f1 - f0)/(2*f1 - f0 - f2)) * w where L = lower class boundary and w = class width