"Histogram" data collection, organization and description PPT courseware

Description

"Histogram" data collection, organization and description PPT courseware

teaching objectives

knowledge and abilities

1. Preliminarily grasp the concept of frequency distribution histogram and be able to draw frequency distribution histogram;

2. Further experience the process of data organization and presentation, and master the method of drawing frequency distribution histograms.

Process and Method

Further manage the process of data organization and presentation, and master the method of drawing frequency distribution histograms.

Emotional attitudes and values

Cultivate statistical awareness in real life and feel the application value of statistical knowledge.

To draw a frequency distribution histogram of a set of data, you can follow the following steps:

(1) Find the range, that is, the difference between the maximum value and the minimum value in the data.

(2) Determine the group distance and number of groups: group distance = range/number of groups.

(3) Grouping, usually for the interval where the values ​​in the group are located, the left closed interval and the right open interval are taken, and the last group is taken as the closed interval.

(4) Register frequencies, calculate frequencies, and list frequency distribution tables.

(5) Draw a frequency distribution histogram. (The vertical axis represents frequency/group distance)

Summarize the method of drawing a histogram:

(1) According to the size of the drawing, draw two mutually perpendicular rays and add arrows at both ends;

(2) On the horizontal ray, appropriately allocate the positions of the bars and determine the width and spacing of the straight bars;

(3) On the ray perpendicular to the horizontal ray, determine the unit length according to the size of the data, and then draw straight bars of different lengths according to the size and note the number.

1. Calculate the difference between the maximum value and the minimum value

In the above data, the minimum value is 56, the maximum value is 88, and their difference is 32, indicating that the range of changes in mathematics competition scores is 32.

2. Determine group spacing and number of groups

Starting from the lowest score, every 5 points is divided into a group, then the maximum value-minimum value/group distance=32/5=62/5

So we need to divide the data into 7 groups, and the number of groups and the distance between groups are 7 and 5 respectively.

in conclusion

The frequency distribution table data is detailed, specific, clear and easy to refer to.

The frequency histogram is intuitive and has a strong contrast effect.

The frequency line chart can reflect the trend of development and change.

Example 1 The picture below is a histogram of the number of sit-ups in a physical fitness test of a class of students in a physical education class. Please answer the following questions according to the picture:

(1) Which group has the most reps?

(2) How many people in the class have done more than 40 sit-ups (including 40 times)?

(3) How many people in the class can do less than 30 sit-ups with their knees bent?

(1) The group with times 30 to 35 has the largest number of people, with 10 people.

(2) Both groups 40~45 and 45~50 are more than 40 times, with a total of 6+6=12 (people).

(3) Both groups 20~25 and 25~30 are less than 30 times, and there are a total of 6+7=13 (people).

Example 2 A store made a histogram of its sales for 300 business days, as shown in the figure below. Please answer the following questions based on the figure:

(1) What percentage of the total business days does the number of days with a turnover of less than 300,000 yuan account for?

(2) How many days have the turnover been less than 300,000 yuan?

(3) How many days did the turnover exceed 400,000 yuan?

(1) As can be seen from the above figure, the percentage of days with a turnover of less than 300,000 yuan to the total business days is 10% + 9% + 28% = 47%.

(2) Since the total business days are 300 days, if the turnover is less than 300,000 yuan, there are 300×47%=141 (days).

(3) Those with a turnover of more than 400,000 yuan account for 12% + 6% + 1% = 19%, so there are 300 × 19% = 57 (days).

Class summary

Through the study of this section, we understand the meaning of frequency distribution and the general steps to obtain the frequency distribution of a set of data:

(1) Calculate the range;

(2) Determine the group distance and number of groups;

(3) Determine points;

(4) List the frequency distribution table;

(5) Draw a frequency distribution histogram.

How to draw a frequency distribution histogram:

(1) How to make a frequency distribution histogram;

(2) There is no standard for group spacing and number of groups. When the data is within 1,000, it is usually divided into 5 to 12 groups;

(3) If you take the midpoint of the upper side of the rectangle, you can get a frequency line chart;

(4) Find the average of the two breakpoints of each group. These averages are called group medians.

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Update Time: 2024-10-22

This template belongs to Mathematics courseware People's Education Press Seventh Grade Mathematics Volume 2 industry PPT template

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