Question

What are the values that make up the 5-number summary? What types of value are they?

Answer 1

A summary consists of five values:

1.Maximum value.

2.Minimum value.

3.Lower quartile

4.Upper quartile

5.median.

These values are presented together and ordered from lowest to highest: minimum value, lower quartile (Q₁), median value (Q₂), upper quartile (Q₃), maximum value.using a box-plot(whisker-plot)

These values have been selected to give a summary of a data set because each value describes a specific part of a data set: the median identifies the centre of a data set; the upper and lower quartiles span the middle half of a data set; and the highest and lowest observations provide additional information about the actual dispersion of the data. This makes the five-number summary a useful measure of spread.

For example:

A year ago, Angela began working at a computer store. Her supervisor asked her to keep a record of the number of sales she made each month:

The following data set is a list of her sales for the last 12 months:

34, 47, 1, 15, 57, 24, 20, 11, 19, 50, 28, 37.

Use Angela's sales records to find:

1. the maximum
2. the minimum
3. the median
4. the lower quartile
5. the upper quartile

Answers

The values in ascending order are:
1, 11, 15, 19, 20, 24, 28, 34, 37, 47, 50, 57

1. Maximum value=57
2. Minimum value=1
3. Median = (12th + first) ÷ 2
   = 6.5th value
   = (sixth + seventh observations) ÷ 2
   = (24 + 28) ÷ 2
   Median= 26
4. Lower quartile = value of middle of first half of data Q₁
   = the median of 1, 11, 15, 19, 20, 24
   = (third + fourth observations) ÷ 2
   = (15 + 19) ÷ 2
   Lower quartile= 17
5. Upper quartile = value of middle of second half of data Q₃
   = the median of 28, 34, 37, 47, 50, 57
   = (third + fourth observations) ÷ 2
   = (37 + 47) ÷ 2
   Upper quartile= 42

FiVE-NUMBER SUMMARY:

MAXIMUM VALUE	57
MINIMUM VALUE	1
MEDIAN	26
LOWER QUARTILE	17
UPPER QUARTILE	42

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