Summary statistics

Summary Statistics

---

How Do you Explain Summary Statistics?

Summary statistics is a part of descriptive statistics that summarizes and provides the gist of information about the sample data.

Statisticians commonly try to describe and characterize the observations by finding:

• a measure of location, or central tendency, such as the arithmetic mean
• a measure of statistical dispersion like the standard mean absolute deviation
• a measure of the shape of the distribution like skewness
• if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient

---

How Do you Analyze Summary Statistics?

In a class, the collection of scores obtained by 30 students is the description of data collected.

To find the mean of the data, we will need to find the average marks of 30 students.

If the average marks obtained by 30 students is 75 out of 100, then we can derive a conclusion or give judgment about the performance of the students on the basis of this result.

Example 1

 

 

The mean monthly salary of 10 workers of a group is $1445

One more worker whose monthly salary is $1500 has joined the group.

Find the mean monthly salary of 11 workers of the group.

Solution

Here, \(n=10, \bar{x}=1445\)

Using the formula,

\begin{align} \bar{x}&=\dfrac{\sum x_i}{n} \\\therefore \sum x_i&= \bar{x} \times n\\\sum x_i&= 1445 \times 10\\&=14450\\\text {10 workers salary} & = $14450\\\text {11 workers salary} & = 14450+1500\\&= $15950\\\text {Average salary} &=\dfrac{15950}{11} \\&= 1450\end{align}

\(  \therefore \text{Average salary of 11 workers}\!= \!$1450\)

Example 2

 

 

The pie chart shows the favorite subjects of students in a class.

Using the information given in the pie chart, determine the percentage of students who chose English.

Solution

We know that \(144^\circ +36^\circ+72^\circ+108^\circ= 360^\circ\)

The percentage of students who chose English \[\begin{align}&=\dfrac{72}{360}\times 100\\&=20\end{align}\]

 

\(\therefore\) The percentage of students who chose English = 20

Example 3

 

 

On World Environment Day, 100 schools decided to plant 100 tree saplings in their gardens.

The following data shows the number of plants that survived in each school after one month.

95	67	28	32	65	65	69	33	98	96
76	42	32	38	42	40	40	69	95	92
75	83	76	83	85	62	37	65	63	42
89	65	73	81	49	52	64	76	83	92
93	68	52	79	81	83	59	82	75	82
86	90	44	62	31	36	38	42	39	83
87	56	58	23	35	76	83	85	30	68
69	83	86	43	45	39	83	75	66	83
92	75	89	66	91	27	88	89	93	42
53	69	90	55	66	49	52	83	34	36

Using this data, can you find the number of schools that were able to retain 50% of the plants or more?

Solution

We need to represent this large amount of data in such a way that a reader can understand it easily.

To include all the observations in groups, we will create various groups of equal intervals.

These intervals are called class intervals.

From this table, it is clear that 50% or more plants survived in (8 + 18 + 10 + 23 + 12) schools.

\(\therefore\) 71 schools were able to retain 50% or more plants in their garden.

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

---

Let's Summarize

This mini-lesson targeted the fascinating concept of summary statistics. The math journey around the summary statistics starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it problems, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.

---

FAQs on Summary Statistics

What is included in summary statistics?

Summary statistics summarize and provide information about the collected data. It characterizes the values in your data set. It tells us where the average lies and whether the data is skewed.

What is the most common summary statistic?

The mean and the median are most commonly used in statistical analysis. 

What is a summary statistic table?

The summary table is a visual representation that summarizes statistical information about data in a tabular form.

What does the five-number summary tell you?

A five-number summary is useful in descriptive analyses or during the initial interpretation of a large data set. It consists of five values: the maximum and minimum values, the lower and upper quartiles, and the median.

What is the purpose of the summary table?

Summary tables are a visual representation of the data making it easier to understand.

What is a summary in math?

Summary in math is a quick and simple description of the data.

How do you describe statistics?

Summary statistics help us to condense the data in a simpler form so that it is easy for us to observe and describe its features at a glance.

What are the types of statistics?

Types of statistics are:

• Descriptive statistics
• Inferential statistics