Question

4             Using your TI-83/4, sketch a histogram of the following data (n = 25; Sx = 1327) and calculate the (a) mean, (b) median, (c) mode and (d) sample standard deviation. (e) How would you describe the shape of the histogram? (pp 56, 58, 89)

               48 59 31 34 35 37 41 46 42 45 47 49 51 52 52 60 61 67 77 75 55 83 53 56 71

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Answer 1

Solution:- Given that samples : 48,59,31,34,35,37,41,46,42,45,47,49,51,52,52,60,61,67,77,75,55,83,53,56,71

a) mean = sum of terms /number of terms = 1327/25 = 53.08

b) median = 52.

Explanation

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

31 34 35 37 41 42 45 46 47 48 49 51 52 52 53 55 56 59 60 61 67 71 75 77 83   

So, the median is 52 .

c) Mode = 52

=> The mode of a set of data is the value in the set that occurs most often.

d) Standard deviation = σ = 13.7354

Step 2: Create the following table. data data-mean -5.08 5.92 -22.08 19.08 18.08 18.08 12.08 25.8084 35.0484 487.5264 384.0484 326.8884 258.5684 145.9284 50.1284 122.7664 85.2884 36.9884 18.8484 4.3284 1.1884 1.1884 47.8384 62.7284 193.7684 572.1684 480.4884 3.8884 895.2084 0.0064 8.5284 321.1284 59 31 37 11.08 8.08 8.08 4.08 2.08 45 47 8.92 7.92 13.92 23.92 21.92 ed 67 75 29.92 0.08 2.92 17.92 83 56 71 Step 3: Find the sum of numbers in the last column to get 2(-x)47184 Step 4: Calculate ơ using the above formula. , Σ(z, x) /4527 84 ' 25-1

e)

Histogram :

30 40 50 60 Histogram (Frequency Diagram) 70 80 90