The table below shows the distribution of the length of 20 iron rods measured in meters

Question

Length:1.0 - 1.1, 1.2 - 1.3, 1.9 - 1.5, 1.6 - 1.7, 1.8 - 1.9,
Frequency 2,3,8,5,2
Using an assured mean of 1.45 calculate the mean of the distribution

Answer 1

To calculate the mean of the distribution using the assured mean method, we follow these steps:

1. Find the midpoint of each interval
2. Calculate the deviation of the midpoint from the assured mean
3. Multiply the deviation by the frequency of the interval
4. Sum these products
5. Divide the sum by the total frequency
6. Add the assured mean to the result.

Step 1: Midpoint of each interval (length):
1.05, 1.25, 1.40, 1.65, 1.85

Step 2: Deviation from the assured mean (1.45):
-0.40, -0.20, -0.05, 0.20, 0.40

Step 3: Multiply the deviation by the frequency:
-0.40 * 2 = -0.80
-0.20 * 3 = -0.60
-0.05 * 8 = -0.40
0.20 * 5 = 1.00
0.40 * 2 = 0.80

Step 4: Sum these products:
-0.80 + (-0.60) + (-0.40) + 1.00 + 0.80 = 0.00

Step 5: Divide the sum by total frequency (20):
0.00 / 20 = 0.00

Step 6: Add the assured mean (1.45) to the result:
1.45 + 0.00 = 1.45

The mean of the distribution is 1.45 meters.