Here is a frequency distribution table (FDT) for a small data set: data valuefrequency14191521162017151813 Find the following measures of central tendency. mean median mode

Step 1 data value(x)frequency(f)Cumulative FrequencyData value(x)×Frequency(f)14191914×19=26615214015×21=31516206016×20=32017157517×15=25518138818×13=234∑(x)=80∑(f)=88∑(x×f)=1390 Step 2 Mean The expression to calculate the mean is, x―=∑(f×x)∑(f) Substitute values in the above expression. x―=139088 =69544 =15.795455 Thus, the of the data is 15.7954455. Step 3 Median The median of the data is the data corresponding to half of the sum of frequencies. Median=x(∑f2) Substitute values in the above expression. Median=x(882) =x(44) From the table, in the cumulative frequency column, the frequencies from 41 to 60 comes corresponds to data x=16. x(f2)=x(44) =x(40&lt;44≤60) =16 Thus, the median of the data is 16. Mode The mode of the data corresponds to data having a high frequency. From the table, the data value 15 has the highest frequency, 21. Thus, the mode of the data is 15.

Step by step solution to "Here is a frequency distribution table (FDT) for..."

philosphy111of

Answered question

2021-11-30

Here is a frequency distribution table (FDT) for a small data set:

\begin{array}{cc} d a t a v a l u e & f r e q u e n c y \\ 14 & 19 \\ 15 & 21 \\ 16 & 20 \\ 17 & 15 \\ 18 & 13 \end{array}

Find the following measures of central tendency.
mean
median
mode

Answer & Explanation

Marlene Broomfield

Beginner2021-12-01Added 15 answers

Step 1
$\begin{array}{cc} d a t a v a l u e (x) & f r e q u e n c y (f) & C u m u l a t i v e F r e q u e n c y & D a t a v a l u e (x) \times F r e q u e n c y (f) \\ 14 & 19 & 19 & 14 \times 19 = 266 \\ 15 & 21 & 40 & 15 \times 21 = 315 \\ 16 & 20 & 60 & 16 \times 20 = 320 \\ 17 & 15 & 75 & 17 \times 15 = 255 \\ 18 & 13 & 88 & 18 \times 13 = 234 \\ \sum (x) = 80 & \sum (f) = 88 & \sum (x \times f) = 1390 \end{array}$
Step 2
Mean
The expression to calculate the mean is,
$\overset{―}{x} = \frac{\sum (f \times x)}{\sum (f)}$
Substitute values in the above expression.
$\overset{―}{x} = \frac{1390}{88}$
$= \frac{695}{44}$
$= 15.795455$
Thus, the of the data is 15.7954455.
Step 3
Median
The median of the data is the data corresponding to half of the sum of frequencies.
$M e d i a n = x (\frac{\sum f}{2})$
Substitute values in the above expression.
$M e d i a n = x (\frac{88}{2})$
$= x (44)$
From the table, in the cumulative frequency column, the frequencies from 41 to 60 comes corresponds to data $x = 16$ .
$x (\frac{f}{2}) = x (44)$
$= x (40 < 44 \leq 60)$
$= 16$
Thus, the median of the data is 16.
Mode
The mode of the data corresponds to data having a high frequency. From the table, the data value 15 has the highest frequency, 21. Thus, the mode of the data is 15.

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