A boy noted the number of taxis passing through a spot on a road for 100 periods each of 3 minutes and summarized it in the table given below.

No. of taxi |
0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-7- | 70-80 |

Frequency |
07 | 14 | 13 | 12 | 20 | 11 | 15 | 08 |

Then the mode is:

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DSSSB TGT Maths Female Subject Concerned - 18 Nov 2018 Shift 3

Option 4 : 44.7

**Concept:**

The mode formula for the grouped data is given by

**\(mode = L + \frac{{{f_0} - {f_1}}}{{2{f_0} - {f_1} - {f_2}}} \times h\)**

L = Lower limit of the modal class

f_{0} = frequency of the modal class

f_{1} = frequency in the class preceding the modal class

f2 = frequency in the class next to the modal class

h = width of the modal class

Modal class is defined as the **class belonging** to the** largest frequency.**

**Given:**

No. of taxi | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |

Frequency | 07 | 14 | 13 | 12 | 20 | 11 | 15 | 08 |

**Calculation:**

Modal class = 40 - 50

L = 40

f_{0} = 20

f_{1} = 12

f_{2} = 11

h = 10

Using the above formula, we can write as

\(mode = 40 + \frac{{20 - 12}}{{2 \times 20 - 12 - 11}} \times 10\)

⇒ \(mode = 40 + \frac{{8 \times 10}}{{17}}\)

⇒ **mode = 40 + 4.7 = 44.7**