Calculate the Mean (x).

Step 1: Calculate the Mean (x). To calculate the mean using the step-deviation method, we first find the class mark (x_i) for each interval, choose an assumed mean (a), calculate u_i = (x_i - a)/(h), and then f_i u_i. The class size (h) is 20-15=5. Let's choose the assumed mean a = 37.5 (the class mark of the 5th class). | Class Interval | f_i | x_i | d_i = x_i - 37.5 | u_i = (d_i)/(5) | f_i u_i | |:---------------|:------|:------|:-------------------|:----------------------|:----------| | 15-20 | 2 | 17.5 | -20 | -4 | -8 | | 20-25 | 4 | 22.5 | -15 | -3 | -12 | | 25-30 | 18 | 27.5 | -10 | -2 | -36 | | 30-35 | 21 | 32.5 | -5 | -1 | -21 | | 35-40 | 33 | 37.5 | 0 | 0 | 0 | | 40-45 | 11 | 42.5 | 5 | 1 | 11 | | 45-50 | 3 | 47.5 | 10 | 2 | 6 | | 50-55 | 6 | 52.5 | 15 | 3 | 18 | | 55-60 | 2 | 57.5 | 20 | 4 | 8 | | Total | f_i = 100 | | | | f_i u_i = -34 | Step 2: Calculate the Mean (x). Using the formula x = a + ( f_i u_i)/( f_i) × h: x = 37.5 + (-34)/(100) × 5 x = 37.5 - (170)/(100) x = 37.5 - 1.7 x = 35.8 The mean is 35.8. Step 3: Calculate the Median (M). First, we calculate the cumulative frequency (C.F.) and find the median class. The total frequency n = f_i = 100, so (n)/(2) = (100)/(2) = 50. | Class Interval | f_i | C.F. | |:---------------|:------|:-----| | 15-20 | 2 | 2 | | 20-25 | 4 | 6 | | 25-30 | 18 | 24 | | 30-35 | 21 | 45 | | 35-40 | 33 | 78 | | 40-45 | 11 | 89 | | 45-50 | 3 | 92 | | 50-55 | 6 | 98 | | 55-60 | 2 | 100 | The cumulative frequency just greater than 50 is 78, which corresponds to the class interval 35-40. This is our median class. From the median class: • Lower limit (l) = 35 • Frequency (f) = 33 • Cumulative frequency of the class preceding the median class (C.F.) = 45 • Class size (h) = 5 Step 4: Calculate the Median (M). Using the formula M = l + [(n)/(2) - C.F.f] × h: M = 35 + [(50 - 45)/(33)] × 5 M = 35 + [(5)/(33)] × 5 M = 35 + (25)/(33) M = 35 + 0.757575... M ≈ 35.76 The median is 35.76. Send me the next one 📸