A survey regarding the heights (in cm) of 50 girls of class X of a school was conducted and the following data was obtained : | Height (in cm) | Number of girls | |---|---| | 120 - 130 | 2 | | 130 - 140 | 8 | | 140 - 150 | 12 | | 150 - 160 | 20 | | 160 - 170 | 8 | | Total | 50 | Find the mean and mode of the above data.

Step 1: Calculate Class Marks and Mean

To calculate the mean of grouped data, we first find the class mark ($x_i$) for each class interval by taking the midpoint of the interval. Then, we multiply each class mark by its corresponding frequency ($f_i$) to get $f_i x_i$. Finally, we sum all $f_i x_i$ values and divide by the total frequency ($\sum f_i$).

Step 2: Calculate the Mean

Substitute the calculated sum of $f_i x_i$ and the total frequency into the mean formula to find the mean height.

Step 3: Identify Modal Class and Parameters

The modal class is the class interval with the highest frequency. From the given data, the class $150 - 160$ has the highest frequency of 20. We then identify the lower limit ($l$), class size ($h$), frequency of the modal class ($f_1$), frequency of the class preceding the modal class ($f_0$), and frequency of the class succeeding the modal class ($f_2$).

Step 4: Apply Mode Formula

The mode for grouped data is calculated using the formula: $l + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h$. This formula helps to estimate the mode within the modal class.

Step 5: Calculate the Mode

Substitute the identified values into the mode formula and perform the calculations to find the mode.

More from this chapter

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