Find the standard deviation, s, of sample data summarized in the frequency distr

Question

Find the standard deviation, s, of sample data summarized in the frequency distribution table below by using the formula below, where x represents the class midpoint f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviation to the standard deviation obtained from the original list of data values, 11.1. (f-x) nin-1) Interval Frequency 2 1 | 6 20-26 27-33 34-40 41-47 48-54 55-61 39 62-68 34 Standard deviation (Round to one decimal place as needed.)

Explanation / Answer

From the data above the following have been calculated as below

n = 94

Therefore n*(n-1) = 8742 ---- (1)

n * Sum(f * x2) = 94 * 314235 = 29538090 ----- (2)

[Sum(f * x)]2 = 5361 * 5361 = 28740321----- (3)

Substituting these 3 values in the formula

s = Sqrt [(29538090-28740321)/8742] = Sqrt(797769 / 8742) = Sqrt(91.257) = 9.5

Interval frequency x f * x x2 f * x2 20-26 2 23 46 529 1058 27-33 1 30 30 900 900 34-40 6 37 222 1369 8214 41-47 3 44 132 1936 5808 48-54 9 51 459 2601 23409 55-61 39 58 2262 3364 131196 62-68 34 65 2210 4225 143650 Total 94 5361 314235

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.