Mathematics

24/3848–12FE Reference Handbook 10.6 · Engineering Probability and Statistics · p. 64 Dispersion, mean, median, and mode

Handbook formula

Mean, Median, and Mode

X ˉ = \frac{1}{n} \sum X_{i}, X ˉ_{w} = \frac{\sum w _{i} X _{i}}{\sum w _{i}}

p. 64 defines the arithmetic mean, the weighted mean, the median (odd n: the ((n+1)/2)th ordered item; even n: average of the (n/2)th and (n/2+1)th), and the mode (greatest frequency). Sample CV = s/X̄ is on the same page. The lists below are original teaching data. Population σ on this page divides by N; sample s divides by n−1.

$X ˉ$: Arithmetic mean
$X ˉ_{w}$: Weighted mean
$n$: Sample size

Step-by-step solved example

For the ordered sample 4, 9, 9, 11, 17, find the mean, median, and mode.

Ordered sample 4, 9, 9, 11, 17. Mean is 10 (not a data point). Median and mode are both 9.

1. Mean
Sum = 50. n = 5. X̄ = 50/5 = 10.
$X ˉ = 10$
2. Median
n is odd, so the ((5+1)/2)th = 3rd item is 9.
$9$
3. Mode
9 occurs twice; every other value occurs once. Mode = 9. The mean 10 is not a data value.
$9$

Answer: mean 10, median 9, mode 9

8 practice questions

0/8 correct

1.Mean of 4, 9, 9, 11, 17?

2.Median of that odd sample?

3.Mode of 4, 9, 9, 11, 17?

4.Values 10 and 20 with weights 1 and 3. Weighted mean?

5.Even sample 2, 6, 10, 14. Median?

6.For odd n the median is

7.The mode is

8.Sample coefficient of variation on p. 64 is