The table below shows the distribution of examination scores of 50 candidates in a selection test: | Score Class | Frequency (f) | | :---: | :---: | | 10 - 19 | 5 | | 20 - 29 | 9 | | 30 - 39 | 16 | | 40 - 49 | 14 | | 50 - 59 | 6 | Using the cumulative frequency distribution (ogive), what is the esti

The table below shows the distribution of examination scores of 50 candidates in a selecti… — JAMB UTME

The table below shows the distribution of examination scores of $50$ candidates in a selection test:

Score Class	Frequency ( $f$ )
$10 - 19$	$5$
$20 - 29$	$9$
$30 - 39$	$16$
$40 - 49$	$14$
$50 - 59$	$6$

Using the cumulative frequency distribution (ogive), what is the estimated $70^{\text{th}}$ percentile score?

A
$33.1$
$43.1$ Cevap
C
$43.6$
D
$38.1$

Cevap

The estimated

70^{\text{th}}

percentile score is

43.1

The

70^{\text{th}}

percentile corresponds to the score at the

35^{\text{th}}

candidate (

70\%

50

). This falls within the

40 - 49

score class, which has a lower boundary of

39.5

, a frequency of

14

, and a class width of

10

. Interpolating linearly gives

39.5 + \left(\frac{35 - 30}{14}\right) \times 10 = 43.07 \approx 43.1

Adım Adım Çözüm

Construct the cumulative frequency table to find class boundaries and cumulative frequencies.

Cumulative frequencies:

10-19

(

CF = 5

20-29

(

CF = 14

30-39

(

CF = 30

40-49

(

CF = 44

50-59

(

CF = 50

Cumulative frequencies are required to locate the position of the desired percentile.

Determine the rank position of the

70^{\text{th}}

percentile (

P_{70}

Rank position =

\frac{70}{100} \times 50 = 35^{\text{th}}

position.

The

70^{\text{th}}

percentile corresponds to the score below which

70\%

of the total candidates fall.

Identify the class interval containing the

35^{\text{th}}

cumulative frequency and state its parameters.

The target class is

40 - 49

. Parameters: Lower class boundary

L = 39.5

, preceding cumulative frequency

CF_{\text{prev}} = 30

, class frequency

f = 14

, class width

c = 10

Since

30 < 35 \le 44

, the

35^{\text{th}}

entry falls within the

40 - 49

class.

Apply the linear interpolation formula for percentiles from an ogive.

P_{70} = L + \left(\frac{\frac{70N}{100} - CF_{\text{prev}}}{f}\right) \times c = 39.5 + \left(\frac{35 - 30}{14}\right) \times 10 = 39.5 + \frac{50}{14} \approx 43.07 \approx 43.1

This calculates the exact score estimate on the cumulative frequency curve.

Anahtar Kavram

Estimating Percentiles from Grouped Data and Ogives

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru