Math, asked by shifaaps3111, 23 days ago

15- 42, 40, 50, 60, 35, 58, 32 Median is

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Answered by shashichandan2016

Answer:

Step-by-step explanation:

1: The age of the players of a soccer team has been listed as {42,40,50,65,35,58,32}. Apply the median formula and find the median of the given set of numbers.

Solution:

To find the median of the given number of sets {42,40,50,65,35,58,32} we will follow the following steps.

Step 1: Arrange the data items in ascending order. Given set: {42,40,50,65,35,58,32}; Arranged set: {32,35,40,42,50,58,65}.

Step 2: Count the number of observations. Here, the number of observations (n) = 7.

Step 3: Now use the median formula when 'n' is odd, given as,[Median = {(n + 1)/2} th term]

Step 4: Median = [(7 + 1)/2]th term = (8/2)th term = 4th term.

Step 5: Note down the 4th observation from the set {32,35,40,42,50,58,65}. The 4th observation is 42.

Answer: The median of the set {32,35,40,42,50,58,65} is 42.

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Median

Median represents the middle value for any group. It is the point at which half the data is more and half the data is less. Median helps to represent a large number of data points with a single data point. The median is the easiest statistical measure to calculate. For calculation of median, the data has to be arranged in ascending order, and then the middlemost data point represents the median of the data.

Further, the . This is known as the measure of central tendency. The three most common measures of central tendency are mean, median, and mode.

Median = [(n + 1)/2]th term

The median formula for n odd observations

Median Formula When n is Even

The median formula of a given set of numbers say having 'n' even number of observations, can be expressed as:

Median = [(n/2)th term + ((n/2) + 1)th term]/2

median formula used for n even data

Example: The age of the members of a weekend poker team has been listed below. Find the median of the above set.

{42, 40, 50, 60, 35, 58, 32}

Solution:

Step 1: Arrange the data items in ascending order.

Original set: {42, 40, 50, 60, 35, 58, 32}

Ordered Set: {32, 35, 40, 42, 50, 58, 60}

Step 2: Count the number of observations. If the number of observations is odd, then we will use the following formula: Median = [(n + 1)/2]th term

Step 3: Calculate the median using the formula.

Median = [(n + 1)/2]th term

= (7 + 1)/2th term = 4th term = 42

Median = 42

Median Formula for Grouped Data

When the data is continuous and in the form of a frequency distribution, the median is calculated through the following sequence of steps.

Step 1: Find the total number of observations(n).

Step 2: an example to calculate median for grouped data.

Example: Calculate the median for the following data:

Marks 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100

Number of students 5 20 35 7 3

Solution:

We need to calculate the cumulative frequencies to find the median.

Marks Number of students Cumulative frequency

0 - 20 5 0 + 5 5

20 - 40 20 5 + 20 25

40 - 60 35 25 + 35 60

60 - 80 7 60 + 7 67

80 - 100 3 67 + 3 70

N =

∑

= 70

N/2 = 70/2 = 35

Median Class is 40 - 60

l = 40, f = 35, c = 25, h = 20

Using Median formula:

Median

[

−

]

= 40 + [(35 - 25)/35] × 20

= 40 + (10/35) × 20

= 40 + (40/7)

Median of Two Numbers

In an ordered series, the median is the number that is mid-way between the range extremes. It is not

Important Notes on Median:

The above content to find the median has been summarized in the form of the following points.

Median is the central value of data (Positional Average).

Data has to be arranged in ascending/descending order to find the middle value or median.

Not every value is considered while calculating the median.

Median doesn't get affected by extreme points.

Thinking Out of the Box:

Now it's time to apply the learned concepts of the median. Here's a question for you!

Question: Determine the median of the first five whole numbers. In a company, for each of the 10 employees working in a service upgrade process, the number of service upgrades sold are as follows: 34, 26, 30, 21, 25, 12, 18, 20, 19, 15. Find out the median number of service upgrades sold by the 10 employees?