1. Calculate the midpoint for each weight range:
– For 118-126: Midpoint = (118 + 126) / 2 = 122
– For 127-135: Midpoint = (127 + 135) / 2 = 131
– For 136-144: Midpoint = (136 + 144) / 2 = 140
– For 145-153: Midpoint = (145 + 153) / 2 = 149
– For 154-162: Midpoint = (154 + 162) / 2 = 158
– For 163-171: Midpoint = (163 + 171) / 2 = 167
– For 172-180: Midpoint = (172 + 180) / 2 = 176
2. Multiply each midpoint by its corresponding frequency to find the sum of the products.
– (122 * 3) + (131 * 5) + (140 * 9) + (149 * 12) + (158 * 5) + (167 * 4) + (176 * 2)
3. Sum the frequencies to find the total number of data points.
– 3 + 5 + 9 + 12 + 5 + 4 + 2 = 40
4. Calculate the mean (average) by dividing the sum of the products by the total number of data points:
– Mean = (Sum of products) / (Total number of data points)
5. To find the median, you can start by listing the weights in ascending order. Then, locate the middle value. Since there are 40 data points (an even number), the median will be the average of the 20th and 21st values.
– Arrange the midpoints in ascending order: 122, 131, 140, 149, 158, 167, 176.
– The 20th value is 149, and the 21st value is 158.
– Median = (149 + 158) / 2
Now, you can calculate the mean and median based on the given data.