Question

The numbers 1, 2, 4, 4, 2x+1, 5, 5, 6 and 7 are written in
ascending order. If the median is 5, then find x. Hence, find the
mode.

Answer 1

Answer:

→ The median of a data set is the middle term of the observations.

There are 8 terms in the given data, so the median term can be both the fourth and fifth term, which are 4 and 2x+1. But it is given that the median is 5, so 2x + 1 = 5

    2x = 5 - 1

    2x = 4

    x = 4/2

    x = 2

• Therefore, the value of x is 2.

→ The mode in a data is the observation that occurs most frequently in a set of data.

We are given the following data: 1, 2, 4, 4, 5, 5, 5, 6.

Clearly, 5 appears three times, meaning it appears most often in the data.

• Therefore, the mode is 5.

Important terms

So that a set of data becomes easier to read and handle, we use some terms, which are briefly described below:

• Mean

Mean is the average of data. The formula to calculate the mean is:

$\sf{\dfrac{Sum\:of\:all\:observations}{Total\:number\:of\:observations}}$

• Mode

Mode is the number that occurs most often in a set of observations. It becomes easier to find the mode if we organize the observations in ascending order.

• Median

To calculate the median, we actually have to organize the observations in ascending order and identify the term in the middle. In an even set of numbers, we take the median as the the two middlemost numbers or their average.