find the standard deviation for the group of data items. the standard deviation is (round to two decimal…

Explanation:

Step1: Write out the data items

From the stem - and - leaf plot, the data items are (x_1 = 26), (x_2=33), (x_3 = 36), (x_4=43), (x_5 = 46). The number of data items (n = 5).

Step2: Calculate the mean (\bar{x})

The mean formula is (\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}). (\sum_{i=1}^{5}x_i=26 + 33+36 + 43+46=184). (\bar{x}=\frac{184}{5}=36.8).

Step3: Calculate ((x_i-\bar{x})^2) for each (i)

• For (x_1 = 26): ((26 - 36.8)^2=(- 10.8)^2 = 116.64)
• For (x_2=33): ((33 - 36.8)^2=(-3.8)^2 = 14.44)
• For (x_3 = 36): ((36 - 36.8)^2=(-0.8)^2=0.64)
• For (x_4=43): ((43 - 36.8)^2=(6.2)^2 = 38.44)
• For (x_5 = 46): ((46 - 36.8)^2=(9.2)^2 = 84.64)

Step4: Calculate the variance (s^2)

The variance formula for a sample (also used when the population is not specified) is (s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}). (\sum_{i = 1}^{5}(x_i-\bar{x})^2=116.64+14.44 + 0.64+38.44+84.64=254.8). (s^2=\frac{254.8}{4}=63.7).

Step5: Calculate the standard deviation (s)

The standard deviation formula is (s=\sqrt{s^2}). (s=\sqrt{63.7}\approx7.98).

Answer:

(7.98)