Measures of location and spread Worked Solutions — A-Level Maths

Fully worked, step-by-step solutions to A-Level Measures of location and spread questions. See exactly how to solve problems on mean, raw data, median, mode.

meanraw datamedianmoderangefrequency table
A-Level70 questionsStep-by-step solutions
Question 1
2 markseasy
The daily rainfall (in mm) over five days was 4,8,6,10,24, 8, 6, 10, 2. Find the mean daily rainfall.

Worked solution

  1. Add up all the values

    ∑x=4+8+6+10+2=30\sum x = 4+8+6+10+2 = 30

    Find the total of the data values.

  2. Count how many values there are

    n=5n = 5

    There are 55 values in the list.

  3. Divide the total by the number of values

    xˉ=∑xn=305=6\bar{x} = \frac{\sum x}{n} = \frac{30}{5} = 6

    The mean is the total divided by how many values there are.

Answer
xˉ=6 mm\bar{x}=6\text{ mm}
Question 2
2 markseasy
A shop records the number of coats sold on four days as 10,15,20,2510, 15, 20, 25. Find the mean number sold.

Worked solution

  1. Add up all the values

    ∑x=10+15+20+25=70\sum x = 10+15+20+25 = 70

    Find the total of the data values.

  2. Count how many values there are

    n=4n = 4

    There are 44 values in the list.

  3. Divide the total by the number of values

    xˉ=∑xn=704=17.5\bar{x} = \frac{\sum x}{n} = \frac{70}{4} = 17.5

    The mean is the total divided by how many values there are.

Answer
xˉ=17.5\bar{x}=17.5
Question 3
2 markseasy
Five students scored 3,7,7,9,143, 7, 7, 9, 14 on a quiz. Calculate the mean score.

Worked solution

  1. Add up all the values

    ∑x=3+7+7+9+14=40\sum x = 3+7+7+9+14 = 40

    Find the total of the data values.

  2. Count how many values there are

    n=5n = 5

    There are 55 values in the list.

  3. Divide the total by the number of values

    xˉ=∑xn=405=8\bar{x} = \frac{\sum x}{n} = \frac{40}{5} = 8

    The mean is the total divided by how many values there are.

Answer
xˉ=8\bar{x}=8
Question 4
2 markseasy
The masses (in kg) of five parcels are 12,18,9,21,1512, 18, 9, 21, 15. Find the mean mass.

Worked solution

  1. Add up all the values

    ∑x=12+18+9+21+15=75\sum x = 12+18+9+21+15 = 75

    Find the total of the data values.

  2. Count how many values there are

    n=5n = 5

    There are 55 values in the list.

  3. Divide the total by the number of values

    xˉ=∑xn=755=15\bar{x} = \frac{\sum x}{n} = \frac{75}{5} = 15

    The mean is the total divided by how many values there are.

Answer
xˉ=15 kg\bar{x}=15\text{ kg}
Question 5
2 markseasy
Find the median of the data 3,7,8,10,123, 7, 8, 10, 12.

Worked solution

  1. Arrange the data in order

    3,7,8,10,123, 7, 8, 10, 12

    Sort the values from smallest to largest.

  2. Find the position of the median

    n+12=5+12=3\frac{n+1}{2} = \frac{5+1}{2} = 3

    The middle value is the 3\text{th} value.

  3. Read off the median value

    median=8\text{median} = 8

    Identify the value at the median position.

Answer
median=8\text{median}=8

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