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Statistics

Aan Triono avatarAan Triono  included in  category Grade 8
     879 words   4 minutes 
Understanding data and statistics, populations and samples, data presentation, and measures of central tendency and spread.

3.10 Analyze data based on data distribution, mean, median, and mode in order to draw conclusions, make decisions, and make predictions.

4.10 Present and solve problems related to data distribution, mean, median, mode, and data spread in order to draw conclusions, make decisions, and make predictions.

After studying statistics, students are expected to be able to:

  1. analyze data using distribution, mean, median, and mode,
  2. present data in several forms,
  3. solve problems related to data presentation and interpretation.

Data is a collection of datums, and a datum is a single fact.

Example: Ratna measures the heights of five students and obtains the following results.

NameDwiWiliNitaWulanDani
Height (cm)155160158160165

The number 155 cm is one datum. The complete set of results is called data.

From the table above, we can conclude that:

  1. Dani is the tallest,
  2. Dwi is the shortest,
  3. Wili and Wulan have the same height.

Drawing conclusions from data is part of statistics, the science of collecting, processing, and interpreting data.

There are two general types of data:

  1. Quantitative data, which is numerical,
  2. Qualitative data, which describes characteristics or conditions.

In many cases, conclusions are not based on all available data. For example, to test river water quality, a researcher does not need to test all the water in the river.

  • all the water in the river is the population,
  • the water taken for testing is the sample.

The mathematics test scores of 30 students are:

6, 8, 7, 6, 6, 5, 7, 8, 8, 5,
9, 9, 8, 6, 7, 7, 7, 6, 8, 7,
10, 8, 8, 6, 6, 5, 9, 9, 7, 6

In a frequency table:

ScoreTallyNumber of Students
5III3
6IIIII III8
7IIIII II7
8IIIII II7
9IIII4
10I1
Total30

A pictogram uses pictures to represent data.

Example

Population data:

  • Area A = 800 people
  • Area B = 650 people
  • Area C = 700 people

Pictogram:

Pictogram

Bar charts are suitable for categorical data.

Example

CityABCDE
Maximum Temperature (°C)1015151220
Minimum Temperature (°C)2530322735

Vertical bar chart:

Vertical bar chart

Horizontal bar chart:

Horizontal bar chart

Line charts are useful for continuous or periodic data.

Example

MonthJanFebMarAprMayJunJulAugSepOctNovDec
Number of TVs201512101517101015201525

Line chart:

Line chart

Pie charts show the comparison between parts and the whole.

Example

ColorFrequency
White10
Pink4
Red8
Blue8
Yellow5
Green5

Central angles:

White=1040×360∘=90∘Pink=440×360∘=36∘Red=840×360∘=72∘Blue=840×360∘=72∘Yellow=540×360∘=45∘Green=540×360∘=45∘ \begin{aligned} \text{White}&=\frac{10}{40}\times 360^\circ=90^\circ\\ \text{Pink}&=\frac{4}{40}\times 360^\circ=36^\circ\\ \text{Red}&=\frac{8}{40}\times 360^\circ=72^\circ\\ \text{Blue}&=\frac{8}{40}\times 360^\circ=72^\circ\\ \text{Yellow}&=\frac{5}{40}\times 360^\circ=45^\circ\\ \text{Green}&=\frac{5}{40}\times 360^\circ=45^\circ \end{aligned}

Pie chart:

Pie chart

The mean is the sum of all data values divided by the number of data values.

xˉ=x1+x2+⋯+xnn \bar{x}=\frac{x_1+x_2+\cdots+x_n}{n}

Example 1

Data: 8, 8, 6, 7, 6, 7, 9, 9

xˉ=608=7.5 \bar{x}=\frac{60}{8}=7.5

Example 2

The average score of 10 students is 70. After adding Rino’s score, the average becomes 68.

x1+x2+⋯+x10=70068=700+x1111748=700+x11x11=48 \begin{aligned} x_1+x_2+\cdots+x_{10}&=700\\ 68&=\frac{700+x_{11}}{11}\\ 748&=700+x_{11}\\ x_{11}&=48 \end{aligned}

So, Rino’s score is 48.

For frequency data:

xˉ=f1x1+f2x2+⋯+fixif1+f2+⋯+fi \bar{x}=\frac{f_1x_1+f_2x_2+\cdots+f_ix_i}{f_1+f_2+\cdots+f_i}

Example

Weight (xi)(x_i)Frequency (fi)(f_i)fixif_i x_i
42284
433129
44144
454180
Total10437
xˉ=43710=43.7 \bar{x}=\frac{437}{10}=43.7

The mode is the value that appears most often in a data set.

Example

Data:

1, 4, 3, 5, 2, 3, 2, 2, 5, 4, 3, 1

The most frequent value is 2, so the mode is 2.

The median is the middle value of ordered data.

  • For an odd number of data values, the median is the middle value.
  • For an even number of data values, the median is the average of the two middle values.

Example 1

Data: 6, 7, 6, 6, 5, 8, 7

Ordered:

5, 6, 6, 6, 7, 7, 8

Median = 6

Example 2

Data: 7, 7, 10, 8, 6, 6, 7, 8

Ordered:

6, 6, 7, 7, 7, 8, 8, 10

Median=7+72=7 \text{Median}=\frac{7+7}{2}=7

Example 3

Score (xi)(x_i)Frequency (fi)(f_i)
504
605
705
808
902
1001

Total data = 25, so the median position is:

25+12=13 \frac{25+1}{2}=13

The 13th datum is 70, so the median is 70.

The range is the difference between the largest and smallest data values.

Data:

150, 155, 160, 157, 158, 160, 155, 150

Ordered:

150, 150, 155, 155, 157, 158, 160, 160

160−150=10 160-150=10

Quartiles divide ordered data into four equal parts:

  • lower quartile Q1Q_1,
  • middle quartile Q2Q_2,
  • upper quartile Q3Q_3.

Steps:

  1. sort the data,
  2. determine Q2Q_2 or median,
  3. determine Q1Q_1 from the lower half,
  4. determine Q3Q_3 from the upper half.

Example

a. 20, 35, 50, 45, 30, 30, 25, 40, 45, 30, 35
b. 11, 13, 10, 10, 12, 15, 14, 12

Ordered:

a. 20, 25, 30, 30, 30, 35, 35, 40, 45, 45, 50

Q1=30,Q2=35,Q3=45 Q_1=30,\quad Q_2=35,\quad Q_3=45

b. 10, 10, 11, 12, 12, 13, 14, 15

Q1=10+112=10.5Q2=12+122=12Q3=13+142=13.5 \begin{aligned} Q_1&=\frac{10+11}{2}=10.5\\ Q_2&=\frac{12+12}{2}=12\\ Q_3&=\frac{13+14}{2}=13.5 \end{aligned}

That concludes this statistics material.

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Updated on 2026-08-08
 Grade 8 Materials
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