Description

Pie Chart. Histogram. Recurrence Distribution Graph. Total Frequency ... To make a pie graph we have to focus the quantity of degrees relating to ...

Transcripts

Showing Statistical Information Statistical Information might be shown: As a table As an outline As a diagram Frequency Table Pie Chart Histogram Frequency Distribution Graph Cumulative Frequency Distribution Graph

Constructing a Frequency Table Suppose that we record the every day high temperature in Poughkeepsie, NY for the month of September over a time of two years and acquire the accompanying qualities: 87, 85, 79, 75, 81, 88, 92, 86, 77, 72, 75, 77, 81, 80, 77, 73, 69, 71, 76, 79, 83, 81, 78, 75, 68, 67, 71, 73, 78, 75, 84, 81, 79, 82, 87, 89, 85, 81, 79, 77, 81, 78, 74, 76, 82, 85, 86, 81, 72, 69, 65, 71, 73, 78, 81, 77, 74, 77, 72, 68 We wish to present this data as a table

Constructing a Frequency Table The data about the scope of high temperatures in Poughkeepsie in the month of September would be have additionally intending to the peruser if the 60 singular readings were assembled into gatherings called classes. To build a recurrence table, the creator should first choose: The quantity of classes to shape The measure of every class

Constructing a Frequency Table Depending upon the quantity of individual perceptions are available in the information set, the quantity of classes ought to more often than not be some place somewhere around 5 and 10. The size (width) of every class ought to be the same. The width will rely on the quantity of classes and the scope of qualities in the first information set. The quantity of classes and class width ought to be picked so that a sensible number of the information focuses exist in each of the classes (especially the focal classes) Definition: The distinction between the littlest and biggest components in an information set is known as the reach.

Constructing a Frequency Table 87, 85, 79, 75, 81, 88, 92, 86, 77, 72, 75, 77, 81, 80, 77, 73, 69, 71, 76, 79, 83, 81, 78, 75, 68, 67, 71, 73, 78, 75, 84, 81, 79, 82, 87, 89, 85, 81, 79, 77, 81, 78, 74, 76, 82, 85, 86, 81, 72, 69, 65, 71, 73, 78, 81, 77, 74, 77, 72, 68 The high and low readings in the above information set are 65 and 92 Range = 92 – 65 = 27 Let\'s choose to make a table with 6 classes of width 5

Constructing a Frequency Table Lower class limits: 65, 70, 75, 80, 85, 90 Upper class limits: 69, 74, 79, 84, 89, 94 Note! No (discrete) information point can have a place with more than one class. Class limits: 64.5, 69.5, 74.5, 79.5, 84.5, 89.5, 94.5 In a discrete dissemination, the class limits lie in the holes between as far as possible and lower point of confinement of nearby classes. No genuine information point will lie on a class limit. Definition: The class width is the contrast between two progressive class limits (or between two progressive lower limits)

Constructing a Frequency Table Once the quantity of classes and class limits have been resolved, the following occupation is to number what number of the information focuses lie in every class. 87, 85, 79, 75, 81, 88, 92, 86, 77, 72, 75, 77, 81, 80, 77, 73, 69, 71, 76, 79, 83, 81, 78, 75, 68, 67, 71, 73, 78, 75, 84, 81, 79, 82, 87, 89, 85, 81, 79, 77, 81, 78, 74, 76, 82, 85, 86, 81, 72, 69, 65, 71, 73, 78, 81, 77, 74, 77, 72, 68 Class Tally Frequency 65-69 x x x x 6 70-74 x x 11 75-79 x x x x 20 80-84 x x x 13 85-89 x x x 9 90-94 x 1

Constructing a Discrete Frequency Graph Constructing a Frequency Graph from a Frequency Table Use the midpoint of every class to speak to the worth for the class. Class midpoint = (lower class limit + upper limit)/2 In the past recurrence table we get: Class Midpoint Total Frequency 64.5 - 69 .5 67 6 0.100 69.5 – 74.5 72 11 0. 183 74.5 – 79.5 77 20 0.333 79.5 – 84.5 82 13 0.217 84.5 – 89.5 87 9 0.150 89.5 – 94.5 92 1 0.0167

Constructing a Discrete Frequency Distribution Graph Frequency % 42 39 36 33 30 27 24 21 18 15 12 9 6 3 0 x 67 72 77 82 87 92 Temperature

Constructing A Histogram Another method for showing the data contained in the recurrence table is by utilization of an outline. We should investigate the development of a Histogram. Rather than partner the whole weight of the class with a solitary point – the midpoint of the class – as was done in building the discrete recurrence conveyance chart, the histogram is a structured presentation that speaks to the heaviness of the class as a bar reaching out over the class interim.

Frequency % Constructing A Histogram 42 39 36 33 30 27 24 21 18 15 12 9 6 3 0 Temperature 64.5 69.5 74.5 79.5 84.5 89.5 94.5

Other Visual Displays Some information does not normally separate into a generally little number of altered size interims. Inclinations for kinds of frozen yogurt Percentage of individuals acquiring diverse levels of pay

Other Graphical Displays Consider the accompanying arrangement of information: Favorite Ice Cream Flavors Vanilla 40% Chocolate 25% Strawberry 15% Chocolate Chip 10% Pistachio 5% Other 5%

Other Graphical Displays To make a pie outline we have to decide the quantity of degrees comparing to every rate. 100% of the curve of a circle = 360 degrees 40% of 360 = 144 degrees 25% of 360 = 90 degrees 15% of 360 = 54 degrees 10% of 360 = 36 degrees 5% of 360 = 18 degrees

other 5% pistachio 5% Other Graphical Displays Chocolate Chip 10% Vanilla 40% Strawberry 15% Chocolate 25% Favorite Ice Cream Flavors

Scatterplots Consider the accompanying arranged estimations of month to month vitality utilization and normal month to month temperature Electricity Ave. Every day Time period Consumed (kWh) Temp. (F o ) Year 1: Jan/Feb 3375 26 Year 1: Mar/Apr 2661 34 Year 1: May/June 2073 58 Year 1: July/Aug 2579 72 Year 1: Sept/Oct 2858 67 Year 1: Nov/Dec 2296 48 Year 2: Jan/Feb 2812 33 Year 2: Mar/Apr 2433 39 Year 2: May/June 2266 66 Year 2: July/Aug 3128 71

Scatterplots To build a scatterplot of the past table we first match each of the temperature and kWh readings (26, 3375), (34, 2661), (58, 2073), (72, 2579), (67, 2858), (48, 2296), (33, 2812), (39, 2433), (66, 2266), (71, 3128) We will plot these combined qualities as focuses on a chart where the x-pivot will be the temperature perusing and the y-hub, the kWh of power utilized.

Scatterplots From the past information we see that the temperatures range from 26 to 72 degrees, and the vitality utilization ranges from 2073 to 3375 kWh. (26, 3375), (34, 2661), (58, 2073), (72, 2579), (67, 2858), (48, 2296), (33, 2812), (39, 2433), (66, 2266), (71, 3128) While it is alluring to have the scale for both the x and y hub to start at 0 and have the same interim size, that is impractical for these readings. We will give the temperature a chance to scale on the x-pivot start at 0 and be set apart in augmentations of 8 degrees up to 80. The scale for the vitality utilization readings on the y-pivot will begin at 2000 and be set apart in additions of 250 kWh up to 3500.

(58, 2073) (71, 3128) (72, 2579) (67, 2858) (39, 2433) (33, 2812) (48, 2296) (66, 2266) (34, 2661) Scatterplots kWh 3500 3250 3000 2750 2500 2250 2000 x 0 8 16 24 32 40 48 56 64 72 80 Temp F o (26, 3375)