A taxi company recorded the distance ( km ) travelled by each of its drivers one Saturday evening. Distance [ d , km ] f 0 < d ≤ 25 0 25 < d ≤ 50 32 50 < d ≤ 75 102 75 < d ≤ 100 86 100 < d ≤ 125 16 125 < d ≤ 150 4 Construct a cumulative frequency table for this information.

Given data: Distance [ d , km ] f 0 < d ≤ 25 0 25 < d ≤ 50 32 50 < d ≤ 75 102 75 < d ≤ 100 86 100 < d ≤ 125 16 125 < d ≤ 150 4 If the frequency of first class interval is added to the frequency of second class and this sum is added to third class and so on then frequencies so obtained are known as Cumulative Frequency. A table which displays the manner in which cumulative frequencies are distributed over various classes is called a cumulative frequency distribution or cumulative frequency table. Cumulative frequency table for this information: Distance [ d , km ] f Cumulative frequency 0 < d ≤ 25 0 0 25 < d ≤ 50 32 0 + 32 = 32 50 < d ≤ 75 102 0 + 32 + 102 = 134 75 < d ≤ 100 86 0 + 32 + 102 + 86 = 220 100 < d ≤ 125 16 0 + 32 + 102 + 86 + 16 = 236 125 < d ≤ 150 4 0 + 32 + 102 + 86 + 16 + 4 = 240

A taxi company recorded the distance ( km ) travelled by each of its drivers one Saturday evening. Distance [ d , km ] f 0 < d ≤ 25 0 25 < d ≤ 50 32 50 < d ≤ 75 102 75 < d ≤ 100 86 100 < d ≤ 125 16 125 < d ≤ 150 4 Draw a cumulative frequency diagram.

Given data: Distance [ d , km ] f 0 < d ≤ 25 0 25 < d ≤ 50 32 50 < d ≤ 75 102 75 < d ≤ 100 86 100 < d ≤ 125 16 125 < d ≤ 150 4 If the frequency of first class interval is added to the frequency of second class and this sum is added to third class and so on then frequencies so obtained are known as Cumulative Frequency. A table which displays the manner in which cumulative frequencies are distributed over various classes is called a cumulative frequency distribution or cumulative frequency table. Cumulative frequency table for this information: Distance [ d , km ] f Cumulative frequency 0 < d ≤ 25 0 0 25 < d ≤ 50 32 0 + 32 = 32 50 < d ≤ 75 102 0 + 32 + 102 = 134 75 < d ≤ 100 86 0 + 32 + 102 + 86 = 220 100 < d ≤ 125 16 0 + 32 + 102 + 86 + 16 = 236 125 < d ≤ 150 4 0 + 32 + 102 + 86 + 16 + 4 = 240 A curve that represents the cumulative frequency distribution of grouped data on a graph is called a Cumulative Frequency Curve or an Ogive Steps to draw cumulative frequency curve: (i) Draw and mark the horizontal and vertical axes. (ii) Take the cumulative frequencies along the y -axis (vertical axis) and the upper-class limits on the x -axis (horizontal axis). (iii) Against each upper-class limit, plot the cumulative frequencies. (iv) Connect the points with a continuous curve.

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The time, in minutes, taken by $100$ students to reply to their friends on social media is shown as a cumulative frequency curve.

Estimate the median time?(Answer withut units)

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Important Questions on Representing Data: Statistics for Univariate Data

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6H>Q 1

The time, in minutes, taken by $100$ students to reply to their friends on social media is shown as a cumulative frequency curve.

Estimate the interquartile range in time taken to reply.(Answer without units)

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6H>Q 1

The time, in minutes, taken by $100$ students to reply to their friends on social media is shown as a cumulative frequency curve.

$90 %$ of the students replied in $k$ minutes or less. Find $k$ .(Answer without units)

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6H>Q 1

The marks obtained by $100$ students are shown on this cumulative frequency curve. Mark the median point on the cumulative frequency curve? Question Image

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6H>Q 2

The marks obtained by $100$ students are shown on this cumulative frequency curve. Estimate the upper quartile, lower quartile and interquartile range.

Question Image

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6H>Q 2

The marks obtained by $100$ students are shown on this cumulative frequency curve. Estimate the lowest mark needed to be in or above the $80^{th}$ percentile on the cumulative frequency curve.

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IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6H>Q 2

A taxi company recorded the distance $(km)$ travelled by each of its drivers one Saturday evening.

Distance $[d, km]$	$f$
$0 < d \leq 25$	$0$
$25 < d \leq 50$	$32$
$50 < d \leq 75$	$102$
$75 < d \leq 100$	$86$
$100 < d \leq 125$	$16$
$125 < d \leq 150$	$4$

Construct a cumulative frequency table for this information.

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Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6H>Q 3

A taxi company recorded the distance $(km)$ travelled by each of its drivers one Saturday evening.

Distance $[d, km]$	$f$
$0 < d \leq 25$	$0$
$25 < d \leq 50$	$32$
$50 < d \leq 75$	$102$
$75 < d \leq 100$	$86$
$100 < d \leq 125$	$16$
$125 < d \leq 150$	$4$

Draw a cumulative frequency diagram.

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IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6H>Q 3

A taxi company recorded the distance $(km)$ travelled by each of its drivers one Saturday evening.

Distance $[d, km]$	$f$
$0 < d \leq 25$	$0$
$25 < d \leq 50$	$32$
$50 < d \leq 75$	$102$
$75 < d \leq 100$	$86$
$100 < d \leq 125$	$16$
$125 < d \leq 150$	$4$

Estimate the median, interquartile range in the distance travelled by the taxi drivers.(Answer median, interquartile values without units)

The time, in minutes, taken by 100 students to reply to their friends on social media is shown as a cumulative frequency curve. Estimate the median time?(Answer withut units)

Important Questions on Representing Data: Statistics for Univariate Data

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The time, in minutes, taken by $100$ students to reply to their friends on social media is shown as a cumulative frequency curve.

Estimate the median time?(Answer withut units)