In a group of 1000 wage earners the monthly wages of 4 % are below Rs 60 and those of 15 % are u

step 1 Hi, here I have to find the median wage. Let's do this. So, we know that 4 % of owners are below

In a group of 1000 wage earners the monthly wages of 4 % are...

In a group of 1000 wage earners the monthly wages of $4 \%$ are below $\operatorname{Rs} 60$ and those of $15 \%$ are under $\mathrm{Rs} 62.50 .15 \%$ earned $\mathrm{Rs} 95$ and over, and $5 \%$ got
Rs 100 and over. Find the median wage

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Key Concepts

Cumulative Frequency Distribution

A cumulative frequency distribution is a running total of frequencies through the classes or categories of a dataset. It is used to determine how many observations fall below a certain value, which is crucial when identifying the position of the median or other percentiles in grouped data.

Interpolation in Grouped Data

Interpolation in grouped data involves estimating a value within an interval where the exact data points are not individually available. When the median lies within a grouped interval, linear interpolation allows us to approximate its value proportionally based on the cumulative frequency within that interval.

Median

The median is a measure of central tendency that divides a dataset into two equal parts, with half the observations lying below it and half above it. It is a critical indicator of the center of a distribution, particularly when the data is skewed or when extreme values may distort the mean.

Percentiles

Percentiles are values that partition a dataset into 100 equal parts, each representing 1% of the data. The median corresponds to the 50th percentile, which is useful for understanding the relative standing of an observation within the entire distribution.

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