statistics

                                                      Statistics Poem

Oh, statistics, you're a mighty tool,

You help us make sense of the data pool.

Mean, mode, and median, you're a trio so grand,

You help us understand the data in our hand.

Mean

The mean is the average, the sum of all,

Divided by the number of terms, it's a simple call.

It gives us a sense of the central tendency,

A measure of what's typical, it's plain to see.

Mode

The mode is the most frequent, the most common value,

It tells us what's most popular, it's quite a resolve.

It's a good measure of what's typical too,

But it's not as robust as the mean, it's true.

Median

The median is the middle value, when the data's sorted,

It's a good measure of central tendency, when the data's distorted.

It's not affected by outliers, it's quite stable and strong,

A good measure of central tendency, it can't go wrong.

Conclusion

Mean, mode, and median, oh, what a trio,

They help us understand the data, it's a no-brainer, you see.

Whether it's grouped or ungrouped, they're always there,

To help us make sense of the data, and show us what to care.

 FOR HINDI LANGUAGE FRIENDS

अर्थ, माध्य, मोड, और आँकड़ों की कहानी,

संख्या जगत में, यह है गौरव की कहानी।

मीडियन होता वो जो बीच की तरफ आए,

सब संख्याओं को छोड़, यही वही होता सच्चा माध्य।

मोड वो होता है जो सबसे बार आए बार-बार,

आँकड़ों की राहों में, यही वो होता प्यार।

मीन, यानी औसत, सबका बाँटे समान,

संख्या विश्व में, है यह ज्ञान का खजान।

सांख्यिकी विज्ञान, जीवन का एक हिस्सा,

जानकर इसे, मिलेगा सफलता का दिशा।

सबको समझाएं, आँकड़ों का महत्व,

सांख्यिकी की राहों पर, बढ़ें सबका होसला।

इस विज्ञान का सौंदर्य, चित्रित करें वचनों में,

मीन, मोड, मीडियन का, हो यह संगीत आपके दिलों में।

संख्या जगत की यह कहानी, सुनो आप सब,

सांख्यिकी के साथ, बढ़ें हम सब कदम।______________________________________________________

some important statistics formulas:

Measures of Central Tendency:

1. Mean (Average):

   • For a set of "n" data points:
     $\overline{�}=\frac{1}{�}{\sum }_{�=1}^{�}{�}_{�}$

2. Weighted Mean:

   • When each data point has a corresponding weight "w_i":
     $\overline{�}=\frac{{\sum }_{�=1}^{�}({�}_{�}\cdot {�}_{�})}{{\sum }_{�=1}^{�}{�}_{�}}$

3. Median:

   • For an ordered data set, the middle value (or the average of the two middle values for even-sized data).

4. Mode:

   • The most frequently occurring value(s) in a data set.

Measures of Dispersion:

5. Range:

   • The difference between the maximum and minimum values in a data set.

6. Variance:

   • For a set of "n" data points:
     $\text{Var}(�)=\frac{1}{�}{\sum }_{�=1}^{�}({�}_{�}-\overline{�}{)}^2$

7. Standard Deviation:

   • $\text{SD}(�)=\sqrt{\text{Var}(�)}$

8. Coefficient of Variation (CV):

   • $\text{CV}=\frac{\text{SD}(�)}{\overline{�}}\times 100\mathrm{\%}$

Probability Distributions:

9. Binomial Probability:

   • $�(�=�)=\left(\genfrac{}{}{0px}{}{�}{�}\right){�}^{�}(1-�{)}^{�-�}$

10. Normal Distribution:

    • $�(�\le �\le �)={\int }_{�}^{�}\frac{1}{\sqrt{2�}�}{�}^{-\frac{(�-�{)}^2}{2{�}^2}}��$

Correlation and Regression:

11. Correlation Coefficient (r):

    • $�=\frac{\sum ({�}_{�}-\overline{�})({�}_{�}-\overline{�})}{\sqrt{\sum ({�}_{�}-\overline{�}{)}^2\sum ({�}_{�}-\overline{�}{)}^2}}$

12. Linear Regression Equation (y = a + bx):

    • $�=\frac{\sum ({�}_{�}-\overline{�})({�}_{�}-\overline{�})}{\sum ({�}_{�}-\overline{�}{)}^2}$
    • $�=\overline{�}-�\overline{�}$

Hypothesis Testing:

13. Z-Score:

    • $�=\frac{�-�}{�}$

14. T-Test:

    • Used for testing hypotheses about the population mean when the sample size is small or the population standard deviation is unknown.