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Mathematics

The weights of 50 apples were recorded as given below. Calculate the mean weight, to the nearest gram, by the step Deviation Method.

Weight in gramsNo.of apples
80 – 855
85 – 908
90 – 9510
95 – 10012
100 – 1058
105 – 1104
110 – 1153

Measures of Central Tendency

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Answer

We construct the following table, taking assumed mean a = 97.5. Here, c (width of each class) = 5.

Weight in gramsNo.of apples (fi)Class mark (yi)ui = (yi - a)/cfiui
80 – 85582.5-3-15
85 – 90887.5-2-16
90 – 951092.5-1-10
95 – 10012a=97.500
100 – 1058102.518
105 – 1104107.528
110 – 1153112.539
Total∑ fi = 50∑ fi ui = -16

By formula,

Mean=a+c×fiuifi=97.5+5×1650=97.51610=97.51.6=95.996\text{Mean} = a + c \times \dfrac{\sum fiui}{\sum f_i} \\[1em] = 97.5 + 5 \times \dfrac{-16}{50} \\[1em] = 97.5 - \dfrac{16}{10} \\[1em] = 97.5 - 1.6 \\[1em] = 95.9 \approx 96

Hence, mean weight of the apples is 96 g.

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