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# The following table shows the ages of the patients admitted in a hospital during a year:

Age (in years): | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 |

No. of students: | 6 | 11 | 21 | 23 | 14 | 5 |

Find the mode and mean of the data given above. Compare and interpret the two measures of central tendency."

Given:

The ages of the patients admitted in a hospital during a year.

To do:

We have to find the mode and mean of the data given above. Also, we have to compare and interpret the two measures of central tendency.

Solution:

The frequency of the given data is as given below.

We observe that the class interval of 35-45 has the maximum frequency(23).

Therefore, it is the modal class.

Here,

$l=35, h=10, f=23, f_1=21, f_2=14$

We know that,

Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$

$=35+\frac{23-21}{2 \times 23-21-14} \times 10$

$=35+\frac{2}{46-35} \times 10$

$=35+\frac{20}{11}$

$=35+1.81$

$=36.8$

The mode of the given data is 36.8 years.

We know that,

Mean $=\frac{\sum{f_ix_i}}{\sum{f_i}}$

$=\frac{2830}{80}$

$=35.37$

The mean of the given data is 35.37 years.

Hence, we observe that mean is less than the mode in the given data.

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