# What measures are equal in a normal distribution

## What measures are the same in a normal distribution?

**The mean, median, and mode**are equal

The measures are usually equal in a perfectly (normal) distribution.

## Which of the 3 measures of central tendency must be equal in a perfectly normal distribution?

In a perfectly symmetrical, non-skewed distribution

**the mean, median and mode**are equal. As distributions become more skewed the difference between these different measures of central tendency gets larger. The mode is the most commonly occurring value in a distribution, population or sample.## In which distribution mean mode and median are equal?

perfectly symmetrical distribution

In

**a perfectly symmetrical distribution**, the mean and the median are the same. This example has one mode (unimodal), and the mode is the same as the mean and median. In a symmetrical distribution that has two modes (bimodal), the two modes would be different from the mean and median.## Which two parameters define a normal distribution?

The graph of the normal distribution is characterized by two parameters:

**the mean, or average, which is the maximum of the graph and about which the graph is always symmetric**; and the standard deviation, which determines the amount of dispersion away from the mean.## What are the 4 measures of central tendency?

The four measures of central tendency are

**mean, median, mode and the midrange**. Here, mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set.## How do the three measures of central tendency relate to a normal distribution?

The three measures:

**mean, median, and mode**under a normal distribution are all the same. Also, in a positively skewed distribution, the mean is the greatest number, as to the median and mode.## What are the 5 properties of normal distribution?

Properties of a normal distribution

**The mean, mode and median are all equal**. The curve is symmetric at the center (i.e. around the mean, μ). Exactly half of the values are to the left of center and exactly half the values are to the right. The total area under the curve is 1.

## What are the four properties of a normal distribution?

Here, we see the four characteristics of a normal distribution. Normal distributions are

**symmetric, unimodal, and asymptotic, and the mean, median, and mode**are all equal.## How many parameters are needed to fully describe any normal distribution?

The normal distribution has

**two parameters**, the mean and standard deviation.## How do you find a normal distribution of percentages?

Consider the normal distribution N(100, 10). To find the percentage of data below 105.3, that is P(x < 105.3), standartize first: P(x < 105.3) = P ( z < 105.3 − 100 10 ) =

**P(z < 0.53)**. Then find the proportion corresponding to 0.53 in Table A: look for the intersection of the row labeled 0.5 and the column labeled .## What are the 3 measures of variability?

**Measures of variability**

- Range: the difference between the highest and lowest values.
- Interquartile range: the range of the middle half of a distribution.
- Standard deviation: average distance from the mean.
- Variance: average of squared distances from the mean.

## What are the main features of normal distribution?

Normal distributions have key characteristics that are easy to spot in graphs:

**The mean, median and mode are exactly the same**. The distribution is symmetric about the mean—half the values fall below the mean and half above the mean. The distribution can be described by two values: the mean and the standard deviation.## What is the percentile of a normal distribution?

The standard normal distribution can also be useful for computing percentiles . For example, the median is the

…

Computing Percentiles.

**50**, the first quartile is the 25^{th}percentile^{th}percentile, and the third quartile is the 75^{th}percentile.…

Computing Percentiles.

Percentile | Z |
---|---|

90th | 1.282 |

95th | 1.645 |

97.5th | 1.960 |

99th | 2.326 |

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Jul 24, 2016

## How do you find the top 2.5 percent of a normal distribution?

For the given normal distribution, the top 2.5% would be

**scores above 12.87 (1.96 standard deviations above the mean)**. Fred’s score is greater than 12.87, thus he is in the top 2.5% and should get a certificate.## Which measures of center and spread are preferentially used to describe normally distributed data?

In the case that the shape of a given distribution is symmetrical with no outliers, it would be appropriate to use the mean and

**the standard deviation**as measures of center and spread. In all other cases, the median should be used to describe the center of the distribution because it is resistant to outliers.## What is the 80th percentile of the standard normal distribution?

Percentile | z-Score |
---|---|

77 | 0.739 |

78 | 0.772 |

79 | 0.806 |

80 | 0.842 |

## How do you find the 75th percentile of a normal distribution?

This can be found by using

**a z table and finding the z associated with 0.75**. The value of z is 0.674. Thus, one must be . 674 standard deviations above the mean to be in the 75th percentile.## What is the 10th percentile of the standard normal distribution?

Therefore, the 10th percentile of the standard normal distribution is

**-1.28**.## What is the value of 70th percentile in a standard normal distribution?

Percentile | z-Score |
---|---|

68 | 0.468 |

69 | 0.496 |

70 | 0.524 |

71 | 0.553 |

## Is there a difference between the 80th percentile and the lower 80 explain?

Is there a difference between the 80th percentile and the top 80%? … Yes, The 80th percentile means

**80% of the data values are equal or below**. The top 80% means 80% of the values are equal or above.## What is the value of 70th percentile?

The 70th percentile means that

**70% of the scores were below your score**, and 30% were above your score. Your actual score was 82%, which means that you answered 82% of the test questions correctly.