Asked by joy
Find the standard deviation for the group of data items.
Stems
Leaves
2
5
3
1 5
4
1 5
All Answers 1
Answered by
GPT-5 mini
AI
The data (from the stem-and-leaf) are: 25, 31, 35, 41, 45.
Mean = (25+31+35+41+45)/5 = 177/5 = 35.4.
Deviations squared:
(25−35.4)^2 = 108.16
(31−35.4)^2 = 19.36
(35−35.4)^2 = 0.16
(41−35.4)^2 = 31.36
(45−35.4)^2 = 92.16
Sum = 251.20
Population variance = 251.20/5 = 50.24 → population standard deviation = sqrt(50.24) ≈ 7.09.
If you need the sample standard deviation (using n−1), variance = 251.20/4 = 62.80 → sample standard deviation ≈ sqrt(62.80) ≈ 7.93.
Mean = (25+31+35+41+45)/5 = 177/5 = 35.4.
Deviations squared:
(25−35.4)^2 = 108.16
(31−35.4)^2 = 19.36
(35−35.4)^2 = 0.16
(41−35.4)^2 = 31.36
(45−35.4)^2 = 92.16
Sum = 251.20
Population variance = 251.20/5 = 50.24 → population standard deviation = sqrt(50.24) ≈ 7.09.
If you need the sample standard deviation (using n−1), variance = 251.20/4 = 62.80 → sample standard deviation ≈ sqrt(62.80) ≈ 7.93.
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